**> Ranking and Ordering: Introduction**

**> Ranking and Ordering: Solved Examples**

**> Ranking and Ordering: Solved Examples – 2**

**> Ranking and Ordering: Solved Examples – 3**

**> Ranking and Ordering: Solved Examples – 4**

**> Ranking and Ordering: Solved Examples – 5**

**> Ranking and Ordering: Solved Examples – 6**

**> Ranking and Ordering: Solved Examples – 7**

**> Ranking and Ordering: Solved Examples – 8**

**> Ranking and Ordering: Solved Examples – 11**

**> Ranking and Ordering: Solved Examples – 12**

**> Ranking and Ordering: Solved Examples – 13**

**> Ranking and Ordering: Solved Examples – 14**

**> Ranking and Ordering: Solved Examples – 15**

**> Ranking and Ordering: Solved Examples – 16**

**> Ranking and Ordering: Solved Examples – 17**

**Practice Exercise 1: Study the information given below and answer the questions based on it.**

**Six persons A, B, C, D, E, and F have different weights and heights. B is taller than A and E but lighter than A and E. D is taller than B. E is only taller than C and F. Only one person lighter than A. D is heavier than C and E but not the heaviest. The number of persons heavier than F is same as shorter than him. Not more than two persons are heavier than C.**

**1. **Who among the following is shortest in the group?

A. C

B. F

C. E

D. D

E. A

**2.**Who among the following is heaviest in the group?

A. D

B. C

C. F

D. B

E. E

**3. **How many persons are lighter than C?

A. None

B. One

C. Two

D. Three

E. Four

**> B is taller than A and E but lighter than A and E.**

Height: B > A, E

Weight: A, E > B

**> D is taller than B.**

Height: D > B > A, E

**> E is only taller than C and F.**

Height: D > B > A > E > C, F

**> Only one person is lighter than A.**

Weight: E > A > B

**> D is heavier than C and E but not the heaviest.**

This implies F is heaviest.

Weight: F > D > E > A > B

**> The number of persons heavier than F is same as shorter than him.**

Height: D > B > A > E > C > F

**> Not more than two persons are heavier than C.**

Weight: F > D > C > E > A > B

Now let’s answer the questions:

**1. **F is the shortest in the group. **So, B is the correct option.**

**2. **F is the heaviest in the group. **So, C is the correct option.**

**3. **There are three persons: A, B, and E, which are lighter than C. **So, D is the correct option.**

**Practice Exercise 2: Study the information given below and answer the questions based on it.**

**Eight persons A, B, C, D, E, F, G, and H live on an eight-floor building. The ground floor is numbered 1 and the topmost floor is numbered 8. They run in a different meters race, 4200m, 5600m, 6100m, 6800m, 7400m, 7800m, 8200m, and 9400m, but not necessarily in the same order. A, who runs 4200m, lives on an even-numbered floor below 5th floor. The ones who live on 4th and 5th floor run for a total of 12000m. Three persons live between A and C. Two persons live between C and H. Three persons live between H and the one who runs 7400m. Two persons live between G and the one who runs 5600m. D, who runs 6800m, lives above A on an odd-numbered floor. The one who lives just above D runs less than D. B lives above G. The one who lives on 3rd floor runs more than E, who runs more than F. **

**1. **On which floor does the person who runs the highest lives?

A. 1st

B. 2nd

C. 3rd

D. 8th

E. 5th

**2. **How many persons run more than B?

A. 2

B. 3

C. 4

D. 5

E. More than 5

**3. **Which of the following combinations is correct?

A. D – 6100m

B. C – 7th floor

C. A – 4th floor

D. E – 7400m

E. G – 4th floor

**4.** How many meters does H run?

A. 5600m

B. 7800m

C. 9400m

D. 8200m

E. 6100m

**5. **Who among the following lives on the 7th floor?

A. A

B. B

C. D

D. H

E. G

**> A, who runs 4200m, lives on an even-numbered floor below 5th floor.**

There are two possibilities:

**> Three persons live between A and C. Two persons live between C and H. Three persons live between H and the one who runs 7400m. ****D, who runs 6800m, lives above A on an odd-numbered floor.**

**> The ones who live on 4th and 5th floor run for a total of 12000m.**

This is not possible in Case 2 as no one runs a 5200m race. So, we reject this case.

**> B lives above G. The one who lives on 3rd floor runs more than E, who runs more than F.**

This implies E and F do not live on the 3rd floor. Therefore, G lives on the 3rd floor and B lives on the 6th floor.

**> Two persons live between G and the one who runs 5600m.**

**> The one who lives just above D runs less than D.**

This implies C runs for 6100m.

**> The one who lives on 3rd floor runs more than E, who runs more than F.**

This implies G runs for 9400m, E runs for 8200m and F runs for 7400m.

Now let’s answer the questions:

**1. **G runs for 9400m and lives on the 3rd floor. **So, C is the correct option.**

**2. **There are 6 persons who run more than B. **So, E is the correct option.**

**3. ****Option (C) is correct.**

**4. **H runs for 7800m. **So, B is the correct option.**

**5. Option (C) is correct.**

**Practice Exercise 3: Each of the five friends A, B, C, D, and E travels different distances to their workplaces. A travels more than B but less than E. D travels more than only C. The one who travels the most, travels 30km. B travels 15 km to his workplace.**

Who amongst the following possibly travels 5 km to the workplace?

A. A

B. C

C. D

D. E

E. Either C or D

Distance Travelled: E > A > B > D > C

E travels 30 km and B travels 15 km to the workplace. Therefore, either C or D possibly travels 5 km to the workplace. **So, E is the correct option.**

**Practice Exercise 4: Study the information given below and answer the questions based on it.**

**Seven persons A, C, H, J, N, O, and V are arranged in terms of decreasing heights values but with random weights.**

**The height of C is 164 cm. The height of J, 161 cm is exactly in the middle. The lowest weight is 55 kg. All the weights are multiples of 5 kg. O is not the shortest but its weight is highest. H is shorter than only two persons. N’s weight is 65 kg. The lowest height is 157 cm. The person with 80 kg weight is the longest. C is shorter than only one person. V’s weight is 70 kg, which is 5 kg less than H. N is longer than both persons, one who has the highest weight and V. J does not have the lowest weight. There is a difference of 9 cm between the person highest in height and the person highest in weight.**

**1. **What is the possible height of H?

A. 160 cm

B. 162 cm

C. 163 cm

D. Either option B or C

E. 159 cm

**2. **Who among the following is the third shortest?

A. O

B. N

C. H

D. None of them is true

E. Either N or O

**3. **Who among the following has the second-highest weight?

A. N

B. J

C. C

D. A

E. None of them

**> The height of J, 161 cm is exactly in the middle. H is shorter than only two persons. The lowest height is 157 cm. The person with 80 kg weight is the longest. C is shorter than only one person. V’s weight is 70 kg, which is 5 kg less than H. **

**> The height of C is 164 cm.**

**> O is not the shortest but its weight is highest. N is longer than both persons, one who has the highest weight and V. N’s weight is 65 kg. V’s weight is 70 kg.**

**> The lowest weight is 55 kg. All the weights are multiples of 5 kg. J does not have the lowest weight. **

This implies C has the lowest weight. Therefore, the weight of O is 85 kg, and that of J is 60 kg.

Now let’s answer the questions:

**1. **Height of H would be greater than 161 cm and less than 164 cm. Therefore, it can possibly be 162 cm or 163 cm. **So, D is the correct option.**

**2. **N is the third shortest. **So, B is the correct option.**

**3. **A, who weighs 80 kg, has the second-highest weight. **So, D is the correct option.**

**Practice Exercise 5: Read the passage given below and solve the questions based on it.**

**During their stint at IIM Shillong, ten students have opted for various electives named from A to F. In these electives, students are given points on a scale of 1 to 5 points. Points obtained by students can be integral points only.**

**It is also known that not all the electives are taken by all the students and not all the students are taking at least an elective.**

**The range of scores indicates the maximum and minimum scores in that elective by the students who have chosen the elective. However, if the range of the scores is 1-4, then at least one of the students must have got 1 point and at least one student must have got 4 points in that elective.**

**The number of elective takers out of the 10 students is given in the last column.**

**1. **How many students have scored more than 4 points in at least 2 electives?

A. 4

B. 7

C. 2

D. Cannot be determined

**2. **What is the minimum number of students who must have scored less than 2 points in at least one elective?

A. 3

B. 4

C. 2

D. None of these

**3. **Elective C and elective E are merged to form a new elective N. This new elective N will have all those students who have opted elective C and elective E and the scores of each of these electives have been taken into consideration while finding the average of elective N. What is the average score of elective N?

A. 4

B. 3

C. 3.5

D. Cannot be determined

**4. **Elective A and elective B are merged to form a new elective H. This new elective H will be having all those students who have opted elective A and elective B and the scores of each of these electives have been taken into consideration while finding the average of elective H. If none of the students of elective A and elective B are common, then what will be the average score of elective H?

A. 10/3

B. 3

C. 3.5

D None of these

**1. **It is not possible to determine the number of students who scored more than 4 points in at least 2 electives. **So, D is the correct option.**

**2. **

**>** In subject A, one student scored 1 point and the remaining five students scored 4 points each.

**>** In subject C, one student scored 1 point and the remaining six students scored a total of 27 points.

**>** In subject D, the range of scores is 1-2, the total score by the students is 4 and the number of students is 3. Therefore, two students scored 1 point each and the third student scored 2 points.

Since a student can opt for more than one elective, the minimum number of students who have scored less than 2 points in at least one elective is 2. **So, C is the correct option.**

**3. **With the information provided, we cannot determine the average marks of elective N. **So, D is the correct option.**

**4. **It is given to us that none of the students of elective A and elective B are common. Also, elective H has all those students who have opted for elective A and elective B. Therefore, the number of students in elective H = 6 + 3 = 9

Total score by students in elective A = 6 × 3.5 = 21

Total score by students in elective B = 3 × 3 = 9

Therefore, the average score of elective H = (21 + 9)/9 = 10/3

**So, A is the correct option.**